H2MA Remedial _ DRV (RVHS)

Teacher’s copy 1 RVHS H2 Mathematics Remedial Programme Topic: Discrete Random Variables Basic Mastery Questions 1. CJC MYE 9758/2021//Q9 (Parts) A biased red die is such that the probability of any face landing up wards is proportional to the square of the number on that face. The random variable X denotes the score obtained in one throw of this die with ( ) 2P X r kr== , where 1r = , 2, 3, 4, 5, 6, and k is a constant. (i) Find the exact value of k . [2] A second biased die is yellow and the random variable Y denotes the score obtained when the yellow die is thrown once. The probability distribution of Y is y 2 4 6 ( )P Yy= 1 5 2 5 2 5 (ii) Find ( )E Y and show that ( ) 56Var 25Y = . [3] (iii) Given that 1Y and 2Y are two independent observations of Y , find ( )12E YY− and ( )12Var YY− . [2] Answer: (i) 1 91k = (ii) 22 5 (iii) 0, 4.48 2. RI MYE 9758/2021//Q10(i) In a game, a player tosses a fair die, whose faces are numbered from 1 to 6. If the player obtains a 6, he tosses the die a second time, and in this case, his score is the absolute difference of 6 and the second number. Otherwise, his score is the number obtained in the first toss. Let the player’s score be denoted by X. Show that ( ) 7P1 36X == and tabulate the probability distribution of X. [3]

Teacher’s copy 2 Standard Questions 1. HCI MYE 9758/2020//Q8 (Parts) A bag contains 9 numbered balls of identical size. Four of the balls are numbered 3, three of the balls are numbered 4 and two of the balls are numbered 5. In a game, three balls are drawn from the bag at random, without replacement. The random variable S is the sum of the numbers on the three balls drawn. (i) Show that ( ) 25P 12 84S == and find the probability distribution of S. [4] (ii) Show that the probability where the sum of the numbers on the three balls drawn is a multiple of 3 is given by 29 84 . [1] 2. RVHS MYE 9758/2020//Q8 In a funfair game, a game-master set up two boxes with each box containing four cards, numbered 1, 2, 3, 4. A player draws one card at random from each box and his score X, is the product of the numbers on the two cards. (i) Find the probability distribution of X. [2] (ii) Calculate the mean score and the variance exactly. [2] The game-master charges $p for each game. If the player’s score is odd, the player wins a $5 cash voucher. Otherwise, the game ends. (iii) Find the range of values of p for the game to be in favour of the game-master. [2] Answer: (ii) 6.25, 17.1875 (iii) 5 3p